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Wind Turbine Basics

Wind turbines come in a variety of different forms. The fundamental principle is to capture the kinetic energy in the wind and convert it to mechanical energy or electricity for human use.


A brief history of humans using wind power


The origin of wind power dates back thousands of years, with the development of windmills for various purposes. Here's a brief overview of the history of wind turbines and their evolution:


The earliest recorded use of wind power can be traced back to ancient civilizations, particularly in Persia (modern-day Iran) and China. Windmills in these regions were primarily used for tasks such as pumping water, grinding grain, and other mechanical work. These early windmills had a vertical-axis design with wooden blades or sails. The earliest known reference to a windmill in Persia dates back to the 9th century. These early windmills were used for grinding grain and pumping water, primarily for agriculture. In China, windmills were used as far back as the 5th century for pumping water and grinding grain. They featured both vertical-axis and horizontal-axis designs.



Windmills started to gain popularity in Europe during the Middle Ages. By the 12th century, windmills were commonly used in Europe for various purposes, including milling grain and pumping water. European windmills typically had a horizontal-axis design with wooden blades and were often used to harness wind power in rural areas.


The development of wind power technology continued to advance in the 19th century. During this time, windmills were used extensively in the United States for water pumping and agriculture in areas without access to reliable electric or mechanical power.


The transition from traditional windmills to modern wind turbines for electricity generation began in the late 19th and early 20th centuries. In 1887, American inventor Charles F. Brush built a 12 kW wind turbine with a horizontal-axis design in Cleveland, Ohio. This marked one of the first attempts to generate electricity from wind.


The modern wind turbine design that laid the foundation for today's wind power industry is often credited to Danish inventors. In the early 20th century, Danish engineer Poul la Cour developed a series of wind turbines for electricity generation. These early Danish wind turbines featured a horizontal-axis design and were used to power electric generators.


Wind power technology continued to evolve throughout the 20th century, with improvements in turbine design, materials, and efficiency. The oil crisis of the 1970s and growing environmental concerns led to renewed interest in wind power as a source of clean, renewable energy. Today, wind turbines are a major source of electricity generation worldwide, with horizontal-axis turbines being the most common design. They are used to generate electricity for homes, businesses, and grid-scale power generation. Wind power has become a crucial component of the renewable energy mix.




Efficiency


The theoretical maximum efficiency of wind turbines is governed by two fundamental equations: Betz's Law and the Betz coefficient.


Betz's Law, also known as Betz's Limit or Betz's Coefficient, is a fundamental principle that sets the upper limit on the amount of kinetic energy that a wind turbine can extract from the wind. It was formulated by the German physicist Albert Betz in 1919. Betz's Law states that no wind turbine can capture more than 59.3% of the kinetic energy in the wind. This means that the maximum theoretical efficiency of a wind turbine is 59.3%.


Betz's law applies to all Newtonian fluids, including wind. If all of the energy coming from wind movement through a turbine were extracted as useful energy, the wind speed afterward would drop to zero. If the wind stopped moving at the exit of the turbine, then no more fresh wind could get in; it would be blocked. In order to keep the wind moving through the turbine, there has to be some wind movement, however small, on the other side with some wind speed greater than zero. Betz's law shows that as air flows through a certain area, and as wind speed slows from losing energy to extraction from a turbine, the airflow must distribute to a wider area. As a result, geometry limits any turbine efficiency to a maximum of 59.3%.


The Betz coefficient, denoted as Cp, is a measure of the efficiency of a wind turbine in extracting power from the wind. It quantifies the fraction of the kinetic energy in the wind that is converted into mechanical or electrical power. Cp is related to Betz's Law and provides a way to calculate the actual efficiency of a wind turbine relative to its theoretical maximum.


Cp is defined as:

Cp = (Power Extracted by the Wind Turbine) / (0.5 ρ A * V^3)

Where:

  • Cp is the Betz coefficient (efficiency).

  • Power Extracted by the Wind Turbine is the mechanical or electrical power produced by the turbine, in watts

  • ρ (rho) is the air density, in kg/m^3

  • A is the swept area of the wind turbine rotor (the area covered by the spinning blades), in m^2

  • V is the wind velocity, in m/s


The formula above shows that the power output of a wind turbine is a cube function of incoming wind velocity. Thus if you can access a 2x windier location (e.g., 12 m/s versus 6 m/s), this does not simply double the available power output. It octuples it (2^3=8). This explains the industry’s push towards offshore wind, where wind speeds are higher. And the quest for ever-taller towers, to access faster wind speeds at greater heights.


The formula also indicates that the potential power generation of a wind turbine is a square function of its blade length. This is because A = π r^2, where r is the blade length of the turbine. Doubling the blade length from 50 meters to 100 meters might thus increase the potential power output by a factor of four (2^2=4), from around 3MW to 12MW. This explains the industry’s push to ever larger blades using incredible materials such as carbon fiber, glass fiber, and specialist resins.


The Cp of a wind turbine can vary depending on its design and operating conditions. Well-designed modern wind turbines can achieve a Cp of around 0.4 to 0.5, which means they convert 40% to 50% of the kinetic energy in the wind into useful power. This value is less than the theoretical maximum of 59.3% (Betz's Law) due to factors such as aerodynamic losses and wake effects.


Home wind power?


The equation above also shows us why generating electricity from wind power at home is not going to be very effective. First, let's rearrange the equation in terms of the power output of a wind turbine:


P = 0.5 Cp ρ π R^2 V^3


If you put a horizontal axis wind turbine on your roof with a blade length of 1 meter, and we assume a wind speed of 4 m/s and a generous Cp efficiency of 0.3, you can expect power output to be:


Power = 0.5 x 0.3 x 1.225 x 3.142 x (1 x 1) x (4 x 4 x 4) = 37 watts


To put that into perspective, you'd need about 40 of these wind turbines just to power your microwave, or 140 to power your air conditioning.


If you want to make your own electricity at your house, wind is not a good option. A single standard solar PV panel would provide you with as much power as 10 wind turbines that are 6 feet in diameter! While wind power has obvious benefits for grid-scale installations, don't bother with it at your house.



World wind power adoption


As we can see by the charts below, electricity generation from wind started to be used at scale in the mid-2000s. Since then, worldwide capacity has been increasing at a faster rate. Wind electricity generation as of 2022 accounts for over 2,000 terawatt-hours, and wind represents 3.27% of the world's primary energy consumption. The United States gets 4.3% of its primary energy from wind, and Denmark leads the world with 26.2% of its primary energy coming from wind.




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